Finite Group Databasebeta

← C2×#13074330 #14920098

Subgroups — C2×#13074330 #14920098

Order 2816.

7946 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊D11C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4#13074330C2116yesmaximal, direct product factor
5C2×#10622572C214yesmaximal, complemented
6C2×#10622836C214yesmaximal, complemented
7C2×#10622556C211yesmaximal, characteristic, complemented
8C2×#10622860C211yesmaximal, characteristic, complemented
9C2×#10622568C211yesmaximal, characteristic, complemented
10C22×C11×#120C211yesmaximal, characteristic, complemented
11C26×C11C2211yescharacteristic
12C25×D11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yescomplemented
15C23×C22⋊D11—28no—
16C23×C22⋊D11—28no—
17C23×C22⋊D11—28no—
18C23×C22⋊D11C2214yes—
19C23×C22⋊D11C2218yescomplemented
20C23×C22⋊D11C2212yescomplemented
21C24×Dic11C2211yescharacteristic
22C2×C11×#120—28no—
23C2×C11×#120C2218yescomplemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2212yescomplemented
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2212yescomplemented
29C22×C22⋊Dic11C2214yescomplemented
30C2×#66990—28no—
31C2×#66990C2218yescomplemented
32C2×#66988—28no—
33C2×#66988C2218yescomplemented
34C22×(C2×D11)⋊C4C2212yescomplemented
35C22×(C2×D11)⋊C4C2214yescomplemented
36C22×Dic11⋊C4C2212yescomplemented
37#10622860C2218yescomplemented
38#10622836C22132yescomplemented
39C2×C11⋊#95C2214yescomplemented
40#10622572C22132yescomplemented
41#10622568C2218yescomplemented
42#10622556C2218yescomplemented
43C25×C11—24no—
44C25×C11—24no—
45C25×C11—48no—
46C25×C11D418yescomplemented
47C25×C11C2311yescharacteristic
48C25×C11C2312yes—
49C25×C11C2311yescharacteristic
50C25×C11C2314yes—
51C24×D11—24no—
52C24×D11—24no—
53C24×D11—48no—
54C24×D11D418yescomplemented
55C24×D11C2312yes—
56C24×D11C2314yes—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11—24no—
60C22×D4×C11—28no—
61C22×D4×C11—48no—
62C22×D4×C11C2314yes—
63C22×D4×C11C2318yescomplemented
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2312yes—
66C22×C22⋊D11—2128no—
67C22×C22⋊D11—216no—
68C22×C22⋊D11—232no—
69C22×C22⋊D11—216no—
70C22×C22⋊D11—232no—
71C22×C22⋊D11—28no—
72C22×C22⋊D11—216no—
73C22×C22⋊D11—232no—
74C22×C22⋊D11—48no—
75C22×C22⋊D11C23116yes—
76C22×C22⋊D11C2318yescomplemented
77C23×Dic11—24no—
78C23×Dic11—24no—
79C23×Dic11D418yescomplemented
80C23×Dic11C2312yes—
81C23×Dic11C2312yes—
82C23×Dic11C2312yes—
83C23×Dic11C2314yes—
84C11×#120—232no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—28no—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2318yescomplemented
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—28no—
92C2×C22⋊Dic11—48no—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2318yescomplemented
96C2×C22⋊Dic11C23116yescomplemented
97#66990—232no—
98#66988—232no—
99C2×(C2×D11)⋊C4—28no—
100C2×(C2×D11)⋊C4—48no—
101C2×(C2×D11)⋊C4C2318yescomplemented
102C2×(C2×D11)⋊C4C23116yescomplemented
103C2×Dic11⋊C4—28no—
104C2×Dic11⋊C4C2318yescomplemented
105C11⋊#95C23116yescomplemented
106C2×#2613—111nomaximal, Sylow
107C24×C11—28no—
108C24×C11—232no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—28no—
112C24×C11—28no—
113C24×C11—28no—
114C24×C11—28no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—28no—
119C24×C11—432no—
120C24×C11—416no—
121C24×C11—432no—
122C24×C11—432no—
123C24×C11C2×D418yes—
124C24×C11C2×D414yes—
125C24×C11C2×D414yes—
126C24×C11C2×D414yes—
127C24×C11C2×D4116yescomplemented
128C24×C11C2412yes—
129C24×C11C2414yes—
130C24×C11C2412yes—
131C24×C11C2411yescharacteristic
132C23×D11—232no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11—28no—
136C23×D11—28no—
137C23×D11—28no—
138C23×D11—28no—
139C23×D11—432no—
140C23×D11—416no—
141C23×D11—432no—
142C23×D11—432no—
143C23×D11C2×D418yes—
144C23×D11C2×D4116yescomplemented
145C23×D11C2414yes—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—28no—
149C2×D4×C11—216no—
150C2×D4×C11—416no—
151C2×D4×C11—432no—
152C2×D4×C11—416no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—28no—
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C2×C22⋊D11—2128no—
161C2×C22⋊D11—2256no—
162C2×C22⋊D11—232no—
163C2×C22⋊D11—232no—
164C2×C22⋊D11—232no—
165C2×C22⋊D11—216no—
166C2×C22⋊D11—416no—
167C2×C22⋊D11—432no—
168C22×Dic11—232no—
169C22×Dic11—28no—
170C22×Dic11—24no—
171C22×Dic11—28no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—28no—
176C22×Dic11—28no—
177C22×Dic11C2×D418yes—
178C22×Dic11C2×D4116yescomplemented
179C22×Dic11C2414yes—
180C22×Dic11C2414yes—
181C22×Dic11C2414yes—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—216no—
184C22⋊Dic11—216no—
185C22⋊Dic11—28no—
186C22⋊Dic11—28no—
187C22⋊Dic11—416no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—416no—
190Dic11⋊C4—216no—
191C24×D4—111no—
192C22×#123—111no—
193C22×#120—111no—
194C22×#120D1111yescharacteristic, complemented
195#2613—1116no—
196C2×#394—114no—
197C2×#392—114no—
198C2×#381—111no—
199C2×#379—111no—
200C2×#379—111no—
201C23×C11—216no—
202C23×C11—216no—
203C23×C11—216no—
204C23×C11—28no—
205C23×C11—216no—
206C23×C11—232no—
207C23×C11—216no—
208C23×C11—216no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—28no—
212C23×C11—28no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—28no—
217C23×C11—432no—
218C23×C11—4128no—
219C23×C11—432no—
220C23×C11—432no—
221C23×C11—416no—
222C23×C11—416no—
223C23×C11—44no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11#120116yes—
228C23×C11C22×D414yes—
229C23×C11C22×D414yes—
230C23×C11C22×D412yes—
231C23×C11C22×D412yes—
232C23×C11C22×D418yes—
233C23×C11C22×D414yes—
234C23×C11C22×D412yes—
235C23×C11H(5,𝔽2)18yes—
236C23×C11C2511yescharacteristic
237C22×D11—216no—
238C22×D11—232no—
239C22×D11—216no—
240C22×D11—216no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—28no—
244C22×D11—28no—
245C22×D11—432no—
246C22×D11—4128no—
247C22×D11—432no—
248C22×D11—432no—
249C22×D11—416no—
250C22×D11—416no—
251C22×D11C22×D418yes—
252D4×C11—432no—
253D4×C11—416no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—28no—
259C2×C4×C11—44no—
260C2×C4×C11—48no—
261C22⋊D11—2128no—
262C22⋊D11—432no—
263C2×Dic11—216no—
264C2×Dic11—232no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—28no—
270C2×Dic11—28no—
271C2×Dic11—48no—
272C2×Dic11—48no—
273C2×Dic11C22×D418yes—
274C26—111no—
275C26C2×D1111yescharacteristic
276C23×D4—118no—
277C23×D4—114no—
278C23×D4—112no—
279C23×D4—228no—
280C23×D4—228no—
281C23×D4—228no—
282C23×D4C2×D1111yescharacteristic
283C23×D4C2×D1112yescomplemented
284C24×C4—111no—
285C2×#123—118no—
286C2×#123—228no—
287C2×#120—28no—
288C2×#120—118no—
289C2×#120—228no—
290C2×#120C2×D1118yescomplemented
291C22×C4⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—114no—
297C22×C22⋊C4—114no—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4C2×D1112yescomplemented
300#394—1132no—
301#392—1132no—
302#381—118no—
303#379—118no—
304#379—118no—
305C2×#95—114no—
306C22×C11—232no—
307C22×C11—28no—
308C22×C11—28no—
309C22×C11—28no—
310C22×C11—28no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—464no—
314C22×C11—432no—
315C22×C11—48no—
316C22×C11—48no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—88no—
322C22×C11C2×#12018yes—
323C22×C11C2×#12014yes—
324C22×C11#53418yes—
325C22×C11#53418yes—
326C22×C11#53518yes—
327C22×C11C23×D411yescharacteristic
328C22×C11C23×D411yescharacteristic
329C22×C11C23×D411yescharacteristic
330C22×C11C2×H(5,𝔽2)14yes—
331C2×D11—28no—
332C2×D11—28no—
333C2×D11—28no—
334C2×D11—464no—
335C2×D11—432no—
336C2×D11—48no—
337C2×D11—48no—
338C4×C11—42no—
339C4×C11—44no—
340Dic11—28no—
341Dic11—44no—
342Dic11—44no—
343C25—24no—
344C25—24no—
345C25—48no—
346C25—112no—
347C25—118no—
348C25—114no—
349C25—224no—
350C25—224no—
351C25—448no—
352C25C22⋊D1118yescomplemented
353C25C22×D1111yescharacteristic
354C25C22×D1112yes—
355C25C22×D1111yescharacteristic
356C25C22×D1114yes—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—28no—
361C22×D4—48no—
362C22×D4—1116no—
363C22×D4—118no—
364C22×D4—2216no—
365C22×D4—2232no—
366C22×D4—2216no—
367C22×D4—2232no—
368C22×D4—22128no—
369C22×D4—2216no—
370C22×D4—2232no—
371C22×D4—228no—
372C22×D4—448no—
373C22×D4C22×D1114yes—
374C22×D4C22×D1118yescomplemented
375C23×C4—118no—
376C23×C4—114no—
377C23×C4—112no—
378C23×C4—112no—
379C23×C4—112no—
380C23×C4—224no—
381C23×C4—224no—
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384#123—2232no—
385#120—232no—
386#120—2232no—
387C2×C4⋊C4—118no—
388C2×C4⋊C4—228no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—1116no—
396C2×C22⋊C4—1116no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—448no—
402C2×C22⋊C4—448no—
403C2×C22⋊C4C22×D1114yes—
404C2×C22⋊C4C22×D1118yescomplemented
405#95—1116no—
406C2×C11—28no—
407C2×C11—48no—
408C2×C11—82no—
409C2×C11#261318yescomplemented
410C2×C11C22×#12011yescharacteristic
411C2×C11C2×#53412yes—
412C2×C11C2×#53412yes—
413C2×C11C2×#53512yes—
414D11—48no—
415C24—28no—
416C24—232no—
417C24—24no—
418C24—24no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—28no—
423C24—22no—
424C24—22no—
425C24—28no—
426C24—22no—
427C24—416no—
428C24—432no—
429C24—432no—
430C24—432no—
431C24—118no—
432C24—114no—
433C24—1116no—
434C24—2232no—
435C24—228no—
436C24—224no—
437C24—228no—
438C24—228no—
439C24—228no—
440C24—224no—
441C24—4432no—
442C24—4416no—
443C24—4432no—
444C24—4432no—
445C24D4×D1114yes—
446C24D4×D1114yes—
447C24C2×C22⋊D1118yes—
448C24C2×C22⋊D1114yes—
449C24C2×C22⋊D11116yescomplemented
450C24C23×D1112yes—
451C24C23×D1114yes—
452C24C23×D1112yes—
453C24C23×D1111yescharacteristic
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—216no—
458C2×D4—416no—
459C2×D4—432no—
460C2×D4—416no—
461C2×D4—2232no—
462C2×D4—2232no—
463C2×D4—22128no—
464C2×D4—22256no—
465C2×D4—2232no—
466C2×D4—2216no—
467C2×D4—4416no—
468C2×D4—4432no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—118no—
475C22×C4—1116no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—114no—
479C22×C4—2232no—
480C22×C4—228no—
481C22×C4—224no—
482C22×C4—228no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—228no—
487C22×C4—228no—
488C22×C4C23×D1114yes—
489C22×C4C23×D1112yes—
490C4⋊C4—2216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—2216no—
494C22⋊C4—2216no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—4416no—
498C22⋊C4—4416no—
499C11C2×#261311yescharacteristic, complemented, Sylow
500C23—216no—
501C23—216no—
502C23—216no—
503C23—28no—
504C23—216no—
505C23—232no—
506C23—216no—
507C23—216no—
508C23—24no—
509C23—24no—
510C23—28no—
511C23—28no—
512C23—22no—
513C23—22no—
514C23—28no—
515C23—22no—
516C23—432no—
517C23—432no—
518C23—432no—
519C23—4128no—
520C23—416no—
521C23—416no—
522C23—44no—
523C23—48no—
524C23—48no—
525C23—48no—
526C23—118no—
527C23—2232no—
528C23—2216no—
529C23—2216no—
530C23—2216no—
531C23—224no—
532C23—228no—
533C23—228no—
534C23—224no—
535C23—4432no—
536C23—4432no—
537C23—4432no—
538C23—44128no—
539C23—4416no—
540C23—4416no—
541C23#66990116yes—
542C23C2×D4×D1114yes—
543C23C2×D4×D1114yes—
544C23C2×D4×D1112yes—
545C23C2×D4×D1112yes—
546C23#6703718yes—
547C23C22×C22⋊D1118yes—
548C23C22×C22⋊D1114yes—
549C23C22×C22⋊D1112yes—
550C23C24×D1111yescharacteristic
551D4—432no—
552D4—416no—
553D4—22128no—
554D4—4432no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—28no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—118no—
563C2×C4—2232no—
564C2×C4—2216no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—228no—
570C2×C4—228no—
571C2×C4—448no—
572C2×C4—448no—
573C22—28no—
574C22—28no—
575C22—28no—
576C22—232no—
577C22—28no—
578C22—28no—
579C22—28no—
580C22—464no—
581C22—48no—
582C22—48no—
583C22—432no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—42no—
588C22—88no—
589C22—228no—
590C22—228no—
591C22—228no—
592C22—4464no—
593C22—448no—
594C22—448no—
595C22—4432no—
596C22#1062312018yes—
597C22#1062312318yes—
598C22C2×#6699018yes—
599C22C2×#6699014yes—
600C22#1062333518yes—
601C22C22×D4×D1111yescharacteristic
602C22C22×D4×D1111yescharacteristic
603C22C2×#6703714yes—
604C22C23×C22⋊D1111yescharacteristic
605C4—44no—
606C4—42no—
607C4—228no—
608C4—444no—
609C4—444no—
610C2—28no—
611C2—48no—
612C2—82no—
613C2—448no—
614C2#1307433018yesdirect product factor
615C2C22×#6699011yescharacteristic
616C2C2×#1062333512yes—
617C2C2×#1062312012yes—
618C2C2×#1062312312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#120C2
socleC24×C11C24
hypercenterC22×#120D11
hypocenterC11C2×#2613
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C24×C22⋊D11C2semidirect
2. C22×#66988C2semidirect
3. C22×#66990C2semidirect
4. #13074330C2direct (N × H)
5. C2×#10622572C2semidirect
6. C2×#10622836C2semidirect
7. C2×#10622556C2semidirect
8. C2×#10622860C2semidirect
9. C2×#10622568C2semidirect
10. C22×C11×#120C2semidirect
14. C23×D4×C11C22semidirect
19. C23×C22⋊D11C22semidirect
20. C23×C22⋊D11C22semidirect
23. C2×C11×#120C22semidirect
25. C22×C11×C22⋊C4C22semidirect
28. C22×C22⋊Dic11C22semidirect
29. C22×C22⋊Dic11C22semidirect
31. C2×#66990C22semidirect
33. C2×#66988C22semidirect
34. C22×(C2×D11)⋊C4C22semidirect
35. C22×(C2×D11)⋊C4C22semidirect
36. C22×Dic11⋊C4C22semidirect
37. #10622860C22semidirect
38. #10622836C22semidirect
39. C2×C11⋊#95C22semidirect
40. #10622572C22semidirect
41. #10622568C22semidirect
42. #10622556C22semidirect
46. C25×C11D4semidirect
54. C24×D11D4semidirect
63. C22×D4×C11C23semidirect
76. C22×C22⋊D11C23semidirect
79. C23×Dic11D4semidirect
88. C2×C11×C22⋊C4C23semidirect
95. C2×C22⋊Dic11C23semidirect
96. C2×C22⋊Dic11C23semidirect
101. C2×(C2×D11)⋊C4C23semidirect
102. C2×(C2×D11)⋊C4C23semidirect
104. C2×Dic11⋊C4C23semidirect
105. C11⋊#95C23semidirect
127. C24×C11C2×D4semidirect
144. C23×D11C2×D4semidirect
178. C22×Dic11C2×D4semidirect
194. C22×#120D11semidirect
283. C23×D4C2×D11semidirect
290. C2×#120C2×D11semidirect
299. C22×C22⋊C4C2×D11semidirect
352. C25C22⋊D11semidirect
374. C22×D4C22×D11semidirect
404. C2×C22⋊C4C22×D11semidirect
409. C2×C11#2613semidirect
449. C24C2×C22⋊D11semidirect
499. C11C2×#2613semidirect
614. C2#13074330direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C24×C22⋊D112
C22×#669882
C22×#669902
#130743302
C2×#106225722
C2×#106228362
C2×#106225562
C2×#106228602
C2×#106225682
C22×C11×#1202
C2×#261311